We present and analyze a new finite element method for solving interfaceproblems on a triangular grid. The method locally modifies a giventriangulation such that the interfaces are accurately resolved and the maximalangle condition holds. Therefore, optimal order of convergence can be shown.Moreover, an appropriate scaling of the basis functions yields an optimalcondition number of the stiffness matrix. The method is applied to an optimaldesign problem for an electric motor where the interface between differentmaterials is evolving in the course of the optimization procedure.
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